Question

Which table shows that y=−f(x)
results in a reflection over the x-axis?

(1 point)
Responses

x −f(x)
−2
0
−3
1
−6
2
x f left parenthesis x right parenthesis negative 2 0 negative 3 1 negative 6 2

x −f(x)
−2
0
−3
−1
−6
−2
x f left parenthesis x right parenthesis negative 2 0 negative 3 negative 1 negative 6 negative 2

x −f(x)
2 0
3 1
6 2
x f left parenthesis x right parenthesis 2 0 3 1 6 2

x −f(x)
2 0
3 −1
6 −2

goes (2,0) to (3,1) stopping at (6,2)

Answer 1

To identify which table correctly represents the transformation \( y = -f(x) \), we need to check which table reflects the outputs \( f(x) \) in the negative direction, indicating a reflection over the x-axis.

1. For the first response:
- If \( f(x) \) were \( \{ (−2, 0), (−3, 1), (−6, 2) \} \), then \( -f(x) \) would be \( \{ (−2, 0), (−3, -1), (−6, -2) \} \).
- This does not match.

2. For the second response:
- If \( f(x) \) were \( \{ (−2, 0), (−3, −1), (−6, −2) \} \), then \( -f(x) \) would be \( \{ (−2, 0), (−3, 1), (−6, 2) \} \).
- This does not match.

3. For the third response:
- For \( \{ (2, 0), (3, 1), (6, 2) \} \), the corresponding \( -f(x) \) results in \( \{ (2, 0), (3, -1), (6, -2) \} \).
- This does match the outputs given in the response, so this represents a reflection over the x-axis.

4. For the fourth response:
- The outputs do not appear to be reflecting correctly; for \( \{ (2, 0), (3, -1), (6, -2) \} \), this also would not fit the required transformation.

Thus, based on the results, the **third response** accurately indicates that \( y = -f(x) \) is reflecting the given points over the x-axis.

The answer is **the third table**.